Problem: Express this quotient in scientific notation: ${\frac{6.880\times 10^{-3}} {8.0\times 10^{-2}}}$
Start by collecting like terms together. $= {\frac{6.880} {8.0}} \times{\frac{10^{-3}} {10^{-2}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.86 \times 10^{-3\,-\,-2}$ $= 0.86 \times 10^{-1}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.86$ is the same as $8.60 \div 10$ , or $8.60 \times 10^{-1}$ $ = {8.60 \times 10^{-1}} \times 10^{-1} $ $= 8.60\times 10^{-2}$